Answer:
412.3 feet
Step-by-step explanation:
To find the distance from the rental shop to the river, we need to use the formula of the distance between a point and a line:
distance(ax + by + c = 0, (x0, y0)) = |ax0 + by0 + c| / sqrt(a2 + b2)
putting the equation y = (1/4)x + 8 in the form ax + by + c = 0, we have a = 1/4, b = -1 and c = 8, and the point represents x0 = -3 and y0 = 3, so we have:
distance = |(1/4) * (-3) - 1*3 + 8| / sqrt( (1/4)^2 + (-1)^2)
distance = |-3/4 + 5| / 1.0308
distance = 4.25 / 1.0308 = 4.123 units
If each unit in the coordinate plane corresponds to 100 feet, the real distance is:
real distance = distance * 100 = 412.3 feet
